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.999...(repeating) = 1
    #6336698 -

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

Does this means there is a contradiction in our math structure? I always thought of math as a universal language, but the proof that he shows kind of contradicts certain mathametical assumptions doesn't it?


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https://kenaisigh.bandcamp.com/ <- Just completed the 2021 RPM challenge for February - An EP in one month (5 songs or 20 minutes). Check it out!

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Re: .999...(repeating) = 1 [Re: Syle]
    #6336971 -

Where's the contradiction?

That 1 can be written as 1 and as .999 (repeating) isn't a contradiction any more than the fact that 1 can be written as 1 and as 2/2 and as 5/5 and as 1/1, and even as n/n.

Different ways of expressing the same number don't add up (pun, heh) to a contradiction.

contradicts certain mathametical assumptions

Which assumptions?


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

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Re: .999...(repeating) = 1 [Re: Diploid]
    #6337173 -

take his example.

1/3 ~ .333... that is an approximation. it just means .333... goes and goes for infinity.

now you: 1/3*3 = 3/3 = 0.333...*3 = 0.999...repeating. thus 0.999... isn't EXACTLY 1, it's just very very very very close...and will never reach 1, for all of eternity.

but, looking at it from a fractional view, 1/3*3 = 3/3 = which EXACTLY equals 1.

see the contradiction?


--------------------
https://kenaisigh.bandcamp.com/ <- Just completed the 2021 RPM challenge for February - An EP in one month (5 songs or 20 minutes). Check it out!

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Re: .999...(repeating) = 1 [Re: Syle]
    #6337270 -

thus 0.999... isn't EXACTLY 1

Sure it is.

.999 (repeating) is another way of writing EXACTLY 1.

Here's why:

1/3 = .3333333...

and

.3333333... + .3333333... +.3333333... = .9999999...

so by substituting 1/3 for .3333333... you get

1/3 + 1/3 + 1/3 = .9999999...

also, you'll agree that

1/3 + 1/3 + 1/3 = 1

so since 1/3 + 1/3 + 1/3 is equal to both .9999999... and 1 at the same time

.9999999... = 1

Just two different ways of writing the SAME number.


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

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Re: .999...(repeating) = 1 [Re: Syle]
    #6337309 -

You are confusing a number with a representation of a number.

> 1/3 ~ .333... that is an approximation.

No, it is not an approximation, it is exact. 1/3 is exactly equal to 0.3333... (repeating). These are two ways of writing the same number.

Think of it this way...

1/9 = 0.11111...
2/9 = 0.22222...
3/9 = 0.33333...
...
7/9 = 0.77777...
8/9 = 0.88888...
9/9 = 0.99999... (n/n=1, thus 9/9=1=0.999....)


--------------------
Just another spore in the wind.

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Re: .999...(repeating) = 1 [Re: Syle]
    #6337357 -

1/3 ~ .333... that is an approximation. it just means .333... goes and goes for infinity.

I think this is where you're getting stuck.

Here's a similar problem:

What is 1/n as n approaches infinity?

The answer is EXACTLY zero, not approximately zero.

You may think the answer is "an infinitely small number", but there's no such number. Infinity doesn't work that way. There is no number that is infinitely large, just like there is no number that is infinitely small.


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

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Re: .999...(repeating) = 1 [Re: Syle]
    #6337550 -

ahhaha this is great. A true internt forum classic... does .999.... = 1?

Of all the forums Ive visited in all the years, this is the topic that I always see crop up.

BTW, Ill throw my opnion in, .999.... does equal 1, exactaly.

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Re: .999...(repeating) = 1 [Re: DieCommie]
    #6337915 -

no it doesn't.

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Re: .999...(repeating) = 1 [Re: Diploid]
    #6338016 -

Diploid said:
1/3 ~ .333... that is an approximation. it just means .333... goes and goes for infinity.

I think this is where you're getting stuck.

Here's a similar problem:

What is 1/n as n approaches infinity?

The answer is EXACTLY zero, not approximately zero.

You may think the answer is "an infinitely small number", but there's no such number. Infinity doesn't work that way. There is no number that is infinitely large, just like there is no number that is infinitely small.


right on, thanks for clearing that up everyone  :thumbup:


--------------------
https://kenaisigh.bandcamp.com/ <- Just completed the 2021 RPM challenge for February - An EP in one month (5 songs or 20 minutes). Check it out!

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Re: .999...(repeating) = 1 [Re: Syle]
    #6338304 -

So you believe now?  haha good job keeping an open mind.  I thought this was going to grow into a huge thread with math vs philosophy (like usual).

The first time i seen one of these threads I was young and hadn't taken much math.  I was one who didnt believe.  Shortly after though my mind was changed.

:thumbup:

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Re: .999...(repeating) = 1 [Re: DieCommie]
    #6338365 -

this problem very simply:

automatically goes against (many many many) people's instant gut reaction. the only people who believe it's true have seen proofs, but i believe that gut reactions can prove better than written proofs.

.9999 repeated cannot equal 1.

they are right next to eachother though

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6338372 -

zero is not a number! gosh you newbs

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Re: .999...(repeating) = 1 [Re: Seuss]
    #6338416 -

Seuss said:
You are confusing a number with a representation of a number.

> 1/3 ~ .333... that is an approximation.

No, it is not an approximation, it is exact. 1/3 is exactly equal to 0.3333... (repeating). These are two ways of writing the same number.




thats not exactly true. 1/3 is not a number. it is TWO NUMBERS, 1 OVER 3.

.33333 infinity is 1 number! i'm pretty sure that .3333 repeated is impossible to measure/use/compute with because you cannot compute with infinity. infinity cannot be measured or described or written in any exact way because it will instantly disappear.



admittedly, this reeks of paradox, so either its both or neither, or both and neither, probably. maybe neither both nor neither

and oh yeah, there IS an infinitely large "number" but its closer to 1 than 1million.

but forget everything i've said, if your bullocks shitfaced plan of ruining the number 1 is so true, then why do so many innocent kids who have never thought about it before, instantly say NO. if the mathmeticiains have not found a good use for this knowledge, then it is wrong, they made it up, not discovered it

Edited by sleepy (12/05/06 11:32 PM)

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6338642 -

i could go on. i'm impatient to win this thread. i was so pissed when my teacher tried to trick me into this bs

Edited by sleepy (12/06/06 12:11 AM)

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6339229 -

sleepy said:
i could go on. i'm impatient to win this thread. i was so pissed when my teacher tried to trick me into this bs


You done rambling?

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6339295 -

Quote:
sleepy said:if the mathmeticiains have not found a good use for this knowledge, then it is wrong, they made it up, not discovered it

Haha, Id say math is invented not discovered.

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6339432 -

> thats not exactly true. 1/3 is not a number. it is TWO NUMBERS, 1 OVER 3.

If you have a issue viewing the symbol "1/3" as a number, then use the world "value" instead.


--------------------
Just another spore in the wind.

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6339626 -

.9999 repeated cannot equal 1.

Do you agree that 1/3 = .3333... exactly?


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

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Re: .999...(repeating) = 1 [Re: Diploid]
    #6339796 -

whoa. this math is based on circles, right?

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Re: .999...(repeating) = 1 [Re: sleepy]
    #6339847 -

the problem is that .99999999999 is infinitely not 1

picture a circle graph with .999 filled in

now

fill in .9999
now fill in .999999

each time you are adding 1 more step

.9
.99
.999





.99 is .09 bigger than .9

and .9999x where x is whatever place you go to (tenths, hundredths, thousandths), it will be 9/x bigger than the last one

even at 9/infinity, thats still a positive number, you are still adding it on to the previous number, and therefore since you can always add something to it, 1st draft:
its not infinite
2nd draftif it hits 1 then you admit that it would keep going because AS SOON as you put infinity in the equasion it creates so many nines that it equals every number in existence at once and simultaneously (without any fluctuations at any time/point/place in value), which of course, includes 1,

(so, here we see that 1=2) has it been proven?


.9
.99
.999
.9999
.99999
.999999
.9999999

always adding on a fraction of a point, smaller and smaller, but still existing, forever.

infinity goes on forever by definition,


.9999 multiplied by infinity equals 1 (taken from .99999*infinity = 1)

and so if .9999infinity=1 then infinity=1

because .99999infinity is not 1 its infinity. so either 1 is infinity *aswell* or its botched math. its like staring at the dark side of the moon, doesn't matter how close it is you wont see it.

until you agree that a number can be two numbers at once, you cannot use infinity at all, because the math can be off a little bit.

its true that .99999infinity = 1, perhaps
but if that is true then it also equals other numbers

Edited by sleepy (12/06/06 11:53 AM)

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